Article pubs.acs.org/JPCC
Bombarding Graphene with Oxygen Ions: Combining Effects of Incident Angle and Ion Energy To Control Defect Generation Zhitong Bai,† Lin Zhang,† and Ling Liu*,† †
Department of Mechanical and Aerospace Engineering, Utah State University, Logan, Utah 84322, United States ABSTRACT: Ion bombardment is a key physical process in the ion implantation and irradiation of graphene, with important implications for tuning graphene’s electronic properties and for understanding the material’s behavior in irradiative environment. Using molecular dynamics with a reactive force field, this work systematically investigates the influence of the incident angle on the generation of defects and vacancies during the bombardment process. It is found that larger incident angles (between the incident line and the surface of graphene) ranging from 70° to 90° are desired for substitution and single vacancy, whereas smaller incident angles ranging from 30° to 50° are favored for forming double vacancies, multiple vacancies, and in-plane disorder. Oxygen ions with the incident angle of 70° produce the highest probability of ion substitution, and the ions at 40−60 eV and 70° yield the highest quality of doping with minimum other defects. These results demonstrate that bombarding graphene along oblique directions may be a promising approach to effectively and efficiently modify graphene for wide applications in nanoelectronics. The angle/energy-damage relationships developed by this study are expected to guide future efforts in ion implantation and to improve the understanding of various irradiation processes. first create vacancies by high-energy atom/ion bombardment, and then fill these vacancies with the desired dopants. Pan et al.50 performed ion irradiation experiments on graphene using helium ions with energies up to 30 keV and concluded that the damage pattern generated in the graphene depends strongly on the energy of the incident ions. Further, Akcöltekin et al.26 studied the modification of graphene using swift heavy ions with the kinetic energy in the order of 100 MeV. The experiments demonstrated that, at oblique angles, ion irradiation on graphene could result in extended damage in the form of nanohillock chains, which can be utilized to zip open the graphene. In addition to the experimental studies, atomistic simulation has been employed extensively to study the ion bombardment of graphene for improved mechanistic understanding of the physical process. Using classical molecular dynamics (MD) and density functional theory (DFT), Åhlgren et al. systematically studied the influence of ion energy (up to 4000 eV) on the doping of graphene with boron and nitrogen ions to form various carbon−boron/nitrogen hybrid structures.31 By simulating the collision of carbon ions with graphene, Bellido et al.35 discovered the importance of impact site on the production of defects and vacancies. In a later study by Liu et al.,37 reactive force field43 was applied to systematically investigate ion bombardment on graphene by analyzing the effects of ion type (iron, gold, and oxygen), ion energy (up to 1 keV), and impact
1. INTRODUCTION Graphene,1 a monatomic layer made from sp2-bonded carbon atoms, has attracted enormous attention due to its unique mechanical, thermal, and electrical properties.2−6 However, pristine graphene has zero band gap, making it unsuitable for applications that require semiconducting materials. This drawback can be remedied by doping graphene with foreign elements.7−9 During doping, carbon atoms are substituted while other defects and vacancies are generated, which fundamentally changes the electrical properties of the graphene,10−13 enabling its semiconducting capability and a wide range of applications in sensors,14,15 superconductors,16,17 and transistors.18 On the contrary, defects and vacancies in some cases can be damaging. When graphene-based materials are used in the spacecraft traveling in low earth orbit, ions in rarefied atmosphere may collide with graphene at high velocities, leading to significant degradation of the materials’ mechanical properties.19−22 In both the doping and irradiation processes, foreign atoms/ ions collide with the graphene massively, leading to desired or undesired defects and vacancies. The velocity and direction of the incident ions with respect to the graphene may be varied in a wide range, controllably or uncontrollably, which may significantly influence the results of collision. To improve our understanding of both processes, it is critical to fundamentally correlate the generated defects and vacancies with the characteristics of the incident ions. Several experimental9,23−29 and computational studies30−42 have been performed along this direction. Wang et al.9 have experimentally demonstrated that graphene can be doped more efficiently by a two-step process: © XXXX American Chemical Society
Received: October 1, 2015 Revised: November 4, 2015
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DOI: 10.1021/acs.jpcc.5b09620 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C site on the probability, controllability, and quality of defects. The results demonstrated that defects and vacancies could form only in the areas with an electron density over 1.5 e/Å3 higher electron density implies stronger interaction with the projectiles, leading to higher probability of defect/vacancy generation. In all these computational studies, the incident ions were assumed to bombard graphene along the direction perpendicular to the graphene surface. In real doping and irradiation processes, however, the incident angle of the ion can be controlled to be oblique, or it can be uncontrollably random. As an ion bombards graphene at an oblique angle, its velocity can be deposed into a normal component and a transverse component. The transverse velocity in the plane of graphene may have profound effects on the entire bombardment process as revealed in a previous experiment,26 and such effects must be dependent on the angle of incidence. Correlating the incident angle with the defects and vacancies generated in graphene would significantly improve the design of doping experiments and our understanding of various irradiation processes. Such an understanding is, however, currently unavailable and requires systematic computational/experimental investigations. Using molecular dynamics with a reactive force field,44 this study systematically investigates the influence of incident angle on the bombardment of graphene with oxygen ions. A spectrum of the ion energy and various incident angles ranging from 30° to 90° are considered for the incident ion. The results of ion bombardment are described in the context of five damage patterns along with other physical events including reflection, absorption, and transmission. The study allows us to quantitatively pinpoint the effects of incident angle on each of the damage patterns and systematically understand the coupling between the normal and transverse velocity components in influencing these physical processes. The computational study also enables the analysis of the energy transferred to graphene during the collision process, which is found to be a key quantity controlling the probability and intensity of certain damage patterns. It is envisioned that the angle/energy-damage relationship developed by this study will serve as a useful reference for future doping efforts and a basis for understanding some irradiation processes of graphene.
Figure 1. (a) Ion (red) bombardment on graphene at an oblique angle. Five damage patterns: (b) substitution; (c) single vacancy; (d) double vacancies; (e) multiple vacancies; (f) in-plane disorder.
were cured and some bigger damage sites became smaller. Longer relaxation was attempted for selected simulations, and no significant change was observed. It is important to note that ion bombardment on graphene is a transient process that highly depends on the location of the impact site. To account for this effect, 400 simulations were performed for each case with a specific incident angle and a specific ion energy; the impact site was randomized in these simulations and the results were analyzed statistically. When combined with the 34 energy levels and 6 incident angles considered for the incident ion, a total of 81 600 simulations were performed for this study. All simulations were performed using large-scale atomic/molecular massive parallel simulator (LAMMPS).45 Atomic interactions were described by the reactive force field,46 a bond-order-dependent potential considering the relationships between bond order, bond length, and bond energy. Verified against DFT,47 the reactive force field parameters44 used in this study have been demonstrated sufficiently accurate for simulating high-velocity collision between oxygen ions and carbon atoms.22 2.2. Possible Physical Events and Damage Patterns. When an oxygen ion bombards the monolayer graphene, one of the four physical events may be observed: reflection, absorption, transmission, and damage. The “damage” here is a broad term that involves five possibilities, as shown in Figure 1b−f: substitution, single vacancy, double vacancies, multiple vacancies, and in-plane disorder. Substitution appears when a carbon atom is replaced by the incident oxygen ion [Figure 1b].
2. MODELS AND METHODS 2.1. Models and Simulation Details. As illustrated in Figure 1a, the simulation system consists of an incident oxygen (O) ion and a monolayer graphene sheet. The graphene was modeled by 1500 carbon (C) atoms, whose center of mass was constrained to be stationary in the simulation. Periodic boundary conditions were applied in the x and y directions to mimic an infinite sheet of graphene. The incident oxygen ion was initially placed 2 nm away from the graphene to avoid significant nonbonded interaction with the carbon atoms. Before the oxygen ion was allowed to move, the graphene was relaxed by energy minimization, followed by a dynamics simulation of 10 ps at 300 K with the NVT ensemble. The time step was set to be 0.1 fs. Then, the bombardment process was simulated using the NVE ensemble for 1 ps with the time step of 0.01 fs. The incident angle, denoted by θ in Figure 2a, was varied from 90° (perpendicular to graphene) to 30°. The energy of the incident oxygen ion was varied from 1.33 to 1008 eV. After the bombardment took place, the system was simulated for another 10 ps at 300 K using the NVT ensemble for relaxation. During this process, some small damage sites B
DOI: 10.1021/acs.jpcc.5b09620 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 2. (a) Definition of the incident angle, θ. E denotes the energy carried by the ion before collision. (b)−(f) Probabilities of the five damage patterns that may be produced as an oxygen ion bombards graphene at different energy levels (E = 1−1008 eV), along different directions (θ = 90°, 70°, 50°, 40°, 35°, and 30°).
Single vacancy occurs when the ion “knocks out” a carbon atom and the vacancy is not filled by any other atom [Figure 1c]. Double [Figure 1d] and multiple vacancies [Figure 1e] are similar to single vacancy except that more carbon atoms are sputtered. In-plane disorder [Figure 1f] refers to a disorder of carbon atoms in the plane of graphene, while no carbon atom is sputtered. 2.3. Statistical Analysis. As mentioned earlier, 400 simulations were performed for the combination of a specific incident angle and a specific ion energy, to statistically account for the effect of the impact site. Each simulation may demonstrate one or none of the five damage patterns defined above. To find the probability to form a specific damage
pattern, a variable Xji is defined, with i (simulation ID) varied from 1 to 400, and j (type of damage) varied from 1 to 5 (1, substitution; 2, single vacancy; 3, double vacancies; 4, multiple vacancies; 5, in-plane disorder). Xji is equal to 1 if the type-j damage occurred in the ith simulation, and 0 if the damage did not occur. The overall probability of forming the type-j damage in a collision event with a specific incident angle and a specific ion energy is then defined as P(j) = C
1 N
N
∑ Xi j i=1
(1) DOI: 10.1021/acs.jpcc.5b09620 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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The Journal of Physical Chemistry C where N is the number of simulations performed for a specific incident angle and a specific ion energy (N = 400 in this study). P(j) is useful because it characterizes the probability at which the type-j damage may occur in a collision event. However, it does not give information regarding how intense the damage is, particularly for atom sputtering. To allow a quantitative investigation, the following quantity is defined to characterize the sputtering yield (i.e., the average number of sputtered atoms) during a collision event:
larger energy is required. It is also worthy of mentioning that the highest probability of substitution (∼0.6) occurs when E = 63 eV and θ = 70°. It is surprising that the probability of substitution maximizes at 70°, instead of 90°. This result can be attributed to a competition between the interaction time and vertical velocity. As the incident angle decreases (when the ion energy is moderately large), the vertical velocity of the ion decreases, which reduces the probability of ion substitution; meanwhile, the ion is given a longer time to interact with more carbon atoms, which enhances the probability of substitution. Both factors compete and they are balanced at 70°, leading to the largest probability of substitution. As the incident angle further decreases to 30°, the reduction in vertical velocity dominates, leading to nearly no substitution. 3.1.2. Single Vacancy. As the ion energy keeps increasing, the energy carried by the ion after sputtering a carbon atom may be large enough for the ion to overcome the interaction with neighboring carbon atoms and pass through the graphene sheet, leading to a single vacancy. It is therefore predicted that, when the ion energy is at a certain level higher than 63 eV, a single vacancy may become more likely to happen than substitution. This prediction is verified by Figure 2c, which demonstrates that in perpendicular bombardment, single vacancy starts to occur at about 45 eV and its probability maximizes (∼0.4) at about 100 eV (which is higher than 63 eV at which the probability of substitution maximizes). Moreover, similar angle effects are identified for single vacancy and substitution. Among all the angles considered in this study, 70° gives the largest probabilities of single vacancy (∼0.45) and substitution (∼0.6). Different from the substitution case, though, the probability of single vacancy reaches a plateau of about 0.15 when the ion energy exceeds 400 eV, at all angles; by contrast, the probability of substitution diminishes as the ion energy becomes large. In some of the cases forming single vacancy, the sputtered carbon atom and the oxygen ion tend to form a dimer (CO), leaving the graphene together. This usually happens when the ion energy is relatively low. At high ion energy, the ion and the sputtered carbon atom have relatively large difference in velocity, making the formation of a dimer less likely. 3.1.3. Double Vacancies. Double-vacancy represents more severe damage than single-vacancy, and therefore more energy input may be required. As demonstrated in Figure 2d, the probability of double-vacancy maximizes (∼0.3) when E = 133 eV and θ = 35°. More importantly, the angle effect on doublevacancy is found to be distinct from that on single-vacancy and substitution. In the former two types of damage, larger angles induce higher probabilities, but in the case of double-vacancy, larger angles are associated with lower probabilities. The highest probability of double-vacancy is only about 0.13 when θ = 90°, whereas θ = 35° gives 0.3. In other words, smaller angles are favored for the formation of double vacancies, whereas larger angles are desired for the formation of single vacancy and substitution. The observation is understandable because in perpendicular bombardment, the oxygen atom may interact strongly with only 1−2 carbon atoms; however, in the case with oblique bombardment (especially when θ is small), there may be multiple carbon atoms in the trajectory of the incident ion, which increases the probability of sputtering two carbon atoms. C−C and C−O dimers are formed between the sputtered carbon atoms and the oxygen ion, in some of the cases generating double vacancies.
N
S=
∑i = 1 ∑j = 1,2,3,4 mijXij N
(2)
Here, mji is the number of atoms sputtered when the type-j damage is formed in the ith simulation; j is allowed to take 1, 2, 3, and 4 because all these damage patterns may involve atom sputtering.
3. RESULTS AND DISCUSSION 3.1. Effects of Incident Angle and Energy on Damage of a Single Type. On the basis of the 81 600 simulations performed in this study, the probability associated with each type of damage is evaluated and plotted in Figure 2b−f as a function of the incident angle and ion energy. The significant effect of incident angle is identified along with its strong coupling with the effect of ion energy. Some of the key observations include the following: (1) substitution has the highest probability when the incident ion energy is low (E ∼ 60 eV); as the ion energy gradually increases, single vacancy takes over, followed sequentially by double vacancies, multiple vacancies, and in-plane disorder; (2) perpendicular bombardment with θ = 90° only yields significant probabilities for substitution and single vacancy, and all the other types of damage are less important with probabilities below 0.12; however, as the incident angle changes, all types of damage become significant (for example, the probability of in-plane disorder reaches 0.27 when θ = 40°). To understand these observations and other effects of the incident angle and ion energy, the probabilities associated with different types of damage are analyzed individually below with a discussion on the underpinning molecular mechanisms. 3.1.1. Substitution. In most occurrences of substitution, the ion velocity is moderately large, large enough to sputter a carbon atom and small enough to allow the ion to stay in the graphene. In perpendicular bombardment, substitution is found to start when the ion energy exceeds about 25 eV [Figure 2b]. This result is consistent with the displacement threshold for a carbon atom in graphene, which was previously determined to be about 20 eV.48,49 Our prediction is slightly higher due to the sampling of impact sites in the simulations. As the ion energy keeps increasing, the probability of substitution increases and finally achieves its maximum value of 0.56 when the ion energy reaches about 63 eV. Both the maximum probability and the ion energy incurring the maximum probability change significantly as the incident angle is varied. In general, as the incident angle decreases, the maximum probability of substitution first increases and then decreases; and meanwhile, the ion energy incurring the maximum probability keeps increasing. Indeed, when an ion bombards graphene at an oblique angle, its velocity can be decomposed into a horizontal component and a vertical component. Higher energy is therefore required to ensure sufficiently large vertical velocity to sputter a carbon atom; the smaller the incident angle, the D
DOI: 10.1021/acs.jpcc.5b09620 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 3. Energy spectra for five types of damage and various incident angles. Different colors correspond to different levels of probability, as defined in the color bar.
3.1.4. Multiple Vacancies. On the basis of similar reasoning, multivacancy may require even higher ion energy and desire small incident angles as well. This is verified by Figure 2e, where the probability of multivacancy is shown to maximize (∼0.24) when E = 150 eV and θ = 35°; the energy is higher than that required for maximizing the probability of doublevacancy, and the angle is small. 3.1.5. In-Plane Disorder. In-plane disorder is fundamentally different from the other types of damage because no atom is sputtered while multiple carbon atoms are displaced within the plane of the graphene. To incur in-plane disorder, the incident ion should have a small vertical velocity to avoid sputtering carbon atoms, and a large horizontal velocity to displace carbon atoms as it glides on the graphene surface. This implies a small incident angle and a large ion energy. Indeed, as shown in Figure 2f, the probability of in-plane disorder maximizes (∼0.27) when E = 210 eV and θ = 40°; the energy is higher than that required for maximizing any type of damage discussed earlier, and the angle is small. 3.1.6. Energy Spectrum. To summarize the results discussed above, Figure 3 shows the energy spectra associated with the five types of damage and various incident angles. The energy spectra provide a convenient way to systematically reveal the probabilities of different types of damage. The dark red color indicates the highest probability, and the dark blue color corresponds to the lowest probability. For example, substitution is more likely to form when the ion collides at about 80 eV, with an incident angle varying from 50° to 90°. Combining the results and discussions for the five types of damage, we conclude that (1) statistically, increasing ion energy would sequentially lead to substitution, single vacancy, double vacancies, multiple vacancies, and in-plane disorder and (2)
the incident angle plays different roles in the formation of the five types of damage (large angle is favored for substitution and single vacancy and unfavored for the rest). 3.2. Probability of Damage and Its Correlation with Energy Transfer. Figure 4a shows the effects of the incident angle and ion energy on the probability associated with the formation of any damage during ion bombardment. Each curve is equivalent to the sum of all corresponding curves in Figure 2b−f. Interestingly, when the incident angle is between 30° and 50°, the probability of damage is close to 1 at certain energy levels; in other words, damage always forms at these angles and energy levels. In comparison, the maximum probability of damage in perpendicular bombardment is only about 0.78, implying that 22% of the cases are damage-free. From this comparison, it seems that smaller incident angles make the formation of damage more likely. The results can be explained by the concepts of interaction time and energy transfer. As mentioned earlier, interaction time describes how long the ion is given to interact with carbon atoms. In addition to depending on the velocity of the ion, it also depends on the incident angle of the ion. In perpendicular impact, for example, the intention of the ion is to directly pass through the graphene sheet; under such a situation, very short time is given for the ion to interact with the carbon atoms [Figure 4c]. At oblique angles, however, the intended path is inclined, which gives the ion longer time to interact with more carbon atoms. It is hypothesized that different lengths of interaction time would transfer different amounts of energy from the ion to carbon, which then induce different levels of damage. To verify this hypothesis, an energy transfer ratio is defined equal to the amount of energy transferred to the graphene by the ion divided by the total energy carried by the E
DOI: 10.1021/acs.jpcc.5b09620 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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Figure 5. Probability of damage versus incident angle plotted for different levels of ion energy varied (a) from 75 to 151 eV and (b) from 252 to 1008 eV.
of ion energy. This can be understood on the basis of the competition between the vertical energy and interaction time. At low energy, the two factors compete: as the incident angle decreases, the vertical energy decreases, which reduces the probability of damage, and the interaction time increases which enhances the probability of damage; at 40−50°, the two factors are balanced, which maximizes the probability of damage. At high energy, however, the vertical energy is sufficiently large at any incident angle: it can easily exceed the threshold energy for displacing carbon atoms, and therefore, the factor of interaction time dominates; as the incident angle increases, interaction time decreases, which reduces the probability of damage. 3.3. Intensity of Damage. The preceding discussion is mainly focused on the probability of damage which, however, gives no information regarding the intensity of damage. To provide a quantitative measure of the intensity of damage, we have defined the sputtering yield using eq 2. The quantity is evaluated for all the simulations performed in this study, and the results are plotted in Figure 6 against the ion energy. In general, it is found that ions bombarding at oblique angles sputter more carbon atoms; and the atom sputtering maximizes when θ = 40° and E = 133 eV. To investigate from a different perspective, the results are replotted in Figure 7 against angle. The effects of angle are shown to be distinct in the low energy range (75−133 eV) and in the medium energy range (169−300 eV), demonstrating strong coupling between the effects of incident angle and ion energy (data with higher energies are not plotted due to the low sputtering yields). Before 133 eV, the sputtering yield first increases and then decreases with the incident angle; after 169 eV, the sputtering yield decreases
Figure 4. (a) Probability of damage (including damage of all types) versus ion energy plotted for six different incident angles. (b) Energy transfer ratio versus ion energy plotted for six different incident angles. (c) Schematic illustration of the intended trajectories of an ion (red) bombarding graphene (gray) at different angles. Red lines show the segments where the ion experiences intense interaction with the carbon atoms.
ion before collision. This quantity is calculated for all the simulations performed in this study, and the results are plotted in Figure 4b. Comparing panels a and b of Figure 4 identifies strong correlation between the energy transfer ratio and the damage formation probability. At smaller angles, particularly 50°, there is a wide spectrum of ion energy that can lead to efficient energy transfer (with the energy transfer ratio >90%), which partly explains why damage is more likely to form at oblique angles. To further study the effect of the incident angle, Figure 5 plots the probability of damage as a function of angle for different energy levels. Interestingly, the probability−angle curves are found to have distinct trends when the energy is at the low end (75−151 eV) and at the high end (252−1008 eV). At low energy, the probability of damage maximizes at about 40−50°; at high energy, however, the probability of damage decreases almost monotonously with increasing incident angle. Therefore, the effect of angle is strongly coupled with the effect F
DOI: 10.1021/acs.jpcc.5b09620 J. Phys. Chem. C XXXX, XXX, XXX−XXX
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and in-plane disorder may form in addition to ion substitution. The objective of most doping processes, however, is to yield doped materials with minimum other defects. To study the effect of the incident angle on the quality of doped graphene, a substitution ratio is defined equal to the probability of substitution divided by the probability of all damage; the higher the substitution ratio, the higher the doping quality. Figure 8 plots the substitution ratio for all angles and energy
Figure 6. Sputtering yield versus ion energy plotted for six different incident angles.
Figure 8. Substitution ratio versus ion energy plotted for six incident angles.
levels considered in this study. The highest substitution ratio (∼0.97) appears when θ = 70° and E = 42 eV; under this condition, the occurrences of other types of damage are limited to below 3%, indicating very high quality of doping. With Figure 8, the conditions associated with high doping quality may be easily identified. Among the ranges of angle and energy considered in this study, two angles are found to be suitable for doping graphene with oxygen (with the substitution ratio >0.8), including 90° with the ion energy between 50 and 57 eV, and 70° with the ion energy between 35 and 55 eV. It deserves mentioning that, to optimize the doping process, both productivity [Figure 2b] and quality of substitution [Figure 8] need to be considered, and due to the complexity of the bombardment process, productivity and quality often trade off each other. 3.5. Probability of Absorption, Reflection, Transmission, and Damage. Sections 3.1−3.4 are focused on the probability and intensity of damage with implications for doping and irradiation. In addition to damage, ion bombardment may also lead to the absorption, reflection, and transmission of the incident ions, depending on the incident angle and ion energy. To better understand the process, Figure 9 plots the probabilities associated with the four physical events that may occur in perpendicular bombardment. When the ion energy is very low (
